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We developed an electrooptic (EO) sensing system using an external optical intensity modulator for radio frequency (RF) electric near-field measurements. This low-noise, high-frequency resolution system is based on the photonic heterodyning technique in which a RF near-field signal is mixed with modulated light by an EO crystal and downconverted to the difference frequency. Because the optical modulator has a bandwidth extending from DC to several gigahertz, the frequency resolution of this system is determined by that of the RF synthesizer it uses. The intensity noise of the modulated light is quite low, and the noise level of the EO signal can be reduced to almost the shot-noise level by using a balanced detection scheme.